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A254569
The number of unordered pairs (f,g) of functions from {1..n} to itself such that fg=gf (i.e., f(g(i))=g(f(i)) for all i).
1
1, 7, 84, 1540, 37345, 1145376, 42402871, 1849021504, 93217426857, 5363120671120, 348669188664511, 25418305492373520, 2064813985107357445, 185896884170249831320, 18459391640792004885375, 2012607682674617326564096, 239898601216105901349115537, 31132586664410794285693925664, 4380971763246528510240944123071, 665896706682993760478978112600400
OFFSET
1,2
FORMULA
a(n) = (A181162(n) - n^n)/2 + n^n.
EXAMPLE
The a(2) = 7 pairs of maps [2] -> [2] are:
01: [ 1 1 ] [ 1 1 ]
02: [ 1 1 ] [ 1 2 ]
03: [ 1 2 ] [ 1 2 ]
04: [ 1 2 ] [ 2 1 ]
05: [ 1 2 ] [ 2 2 ]
06: [ 2 1 ] [ 2 1 ]
07: [ 2 2 ] [ 2 2 ]
CROSSREFS
Cf. A181162 (ordered pairs), A254570 (unordered pairs, f and g distinct).
Sequence in context: A172455 A258174 A370934 * A183177 A367351 A058795
KEYWORD
nonn
AUTHOR
Joerg Arndt, Feb 01 2015
STATUS
approved